1. SOLID STATE
CHEMISTRY

2. contents Introduction Types of solids Crystal Structures
Elements of Symmetry
Bragg’s equation
Allotropes of carbon: Diamond, graphite & Fullerene

3. INTRODUCTION Three phases of matter: Gas Liquid Solid

4. Gas molecules

5. Liquid molecules

6. Solid
molecules

7. What is solid? Definite shape. Definite volume. Highly incompressible.
Rigid.
Constituent particles held closely by strong intermolecular forces.
Fixed position of constituents.

8. TYPES OF SOLIDS
Two types (based upon atomic arrangement, binding energy, physical & chemical properties):
Crystalline
Amorphous

9. Crystalline solids
The building constituents arrange themselves in regular manner throughout the entire three dimensional network.
Existence of crystalline lattice.
A crystalline lattice is a solid figure which has a definite geometrical shape, with flat faces and sharp edges.
Incompressible orderly arranged units.
Definite sharp melting point.
Anisotropy.
Definite geometry.
Give x-ray diffraction bands.
Examples: NaCl, CsCl, etc.

10. AMORPHOUS SOLIDS Derived from Greek word ‘Omorphe’ meaning shapeless.
No regular but haphazard arrangement of atoms or molecules.
Also considered as non-crystalline solids or super-cooled liquids.
No sharp m.p.
Isotropic.
No definite geometrical shape.
Do not give x-ray diffraction bands.
Examples: glass, rubber, plastics.

11. Types of crystal structures
Ionic crystals
Covalent crystals
Molecular crystals
Metallic crystals

12. Ionic crystals
Lattice points are occupied by positive and negative ions.
Hard and brittle solids.
High m.p. due to very strong electrostatic forces of attraction.
Poor conductors of electricity in solid state but good in molten state.
Packing of spheres depends upon:
presence of charged species present.
difference in the size of anions and cations.
Two types:
AB types.
AB2 types.

13. Covalent crystals Lattice points are occupied by neutral atoms.
Atoms are held together by covalent bonds
Hard solids.
High m.p.
Poor conductors of electricity.
Two common examples: diamond & graphite.

14. Molecular crystals Lattice points are occupied by neutral molecules.
The molecules are held together by vander Waal’s forces.
Very soft solids.
Low m.p.
Poor conductors of electricity.

15. Metallic crystals
Lattice points are occupied by positive metal ions surrounded by a sea of mobile e-.
Soft to very hard.
Metals have high tensile strength.
Good conductors of electricity.
Malleable and ductile.
Bonding electrons in metals remain delocalized over the entire crystal.
High density.

16. Laws of symmetry Plane of symmetry Centre of symmetry
Axis of symmetry.

17. Elements of symmetry in cubic crystal
Rectangular planes of symmetry: 3
Diagonal planes of symmetry: 6
Axes of four-fold symmetry: 3
Axes of three-fold symmetry: 4
Axes of two-fold symmetry: 6
Centre of symmetry: 1
Total symmetry elements: 23

18. Planes of symmetry Rectangular plane of symmetry: 3
Diagonal plane of symmetry: 6

19. Axis of symmetry Four-fold axis of symmetry: 3
Three-fold axis of symmetry: 4

20. Axis & centre of symmetry
Two-fold axis of symmetry: 6

21. Types of cubic crystals
Four types:
Simple or primitive type
Body-centered
Face-centered
End face-centered

22. Body-centered cell (bcc)
Simple or primitive type (sc)

23. Face-centered cell (fcc)
End face-centered cell

24. Number of atoms per unit cell in a cubic lattice
Simple cubic cell: 1atom/unit cell of sc
Body-centered cell: 2 atoms/unit cell of bcc
Face-centered cell: 4 atoms/unit cell of fcc
End face-centered cell: 2 atoms/unit cell

25. Simple cube
No of atoms per unit cell= 8 x 1/8 = 1

26. No of atoms per unit cell= 8 x 1/8 = 1

27. Simple cubic arrangement
e.g.Polonium
52% of the space is occupied by the atoms

28. Body centered cubic lattice
No of atoms present per unit cell
= (8 x 1/8 ) + (1 x 1) = 2

29. No of atoms per unit cell= (8 x 1/8) +1 = 2

30. Body centered cubic lattice
e.g. CsCl, CsBr
68% of the space is occupied by the atoms

31. Face-centered cubic lattice
No of atoms present per unit cell = (8 x 1/8 ) + (6 x 1/2) = 4

32. Face-centered cubic lattice
e.g. NaCl, NaF, KBr, MgO
74% of the space is occupied by the atoms

33. End face-centered cubic lattice
No of atoms present per unit cell = (8 x 1/8 ) + (2 x 1/2) = 2

34. Atomic radius of a cubic lattice
Simple cubic cell:
r = a/2
Face-centered cubic cell:
r = a/√8
Body-centered cubic cell:
r = √3a/4
(where a → length of cube)

35. Radius ratio rule
Relation between the radius, co-ordination number and the structural arrangement of the molecule.
Radius ratio =
Greater the radius ratio, larger the size of the cation and hence the co-ordination number.
density = (z*Ma)/Na*a^ Ma=mass no.,
Na=avogadro, a= side length, z=no. of atoms

36. Structural analysis by radius ratio rule
S.NO.
RADIUS RATIO
CO-ORDINATION NUMBER
SHAPE
EXAMPLE 1.
0.0 – 0.155 2
Linear
HF- 2.
0.155–0.225 3
Triangular planar
B2O3, BN 3.
0.225– 0.414 4
Tetrahedral
ZnS, SiO4-4 4.
0.414– 0.732 6
Octahedral
NaCl 5.
0.732 – 1.0 8
Body-centered cubic
CsCl

37. BRAVAIS LATTICES Unit cell parameters: Lengths a, b & c.
Angles α, β & γ.
Total crystal lattices: 7
Total Bravais lattices: 14

38. Crystal systems with unit cell parameters
S.No.
System
Cell Dimensions
Crystal Angles
Bravais Lattices
Min. Sym. Elements 1.
Cubic
a = b = c
α=β=γ=90ْ
sc, fcc, bcc = 3
3-fold axes: 4
4-fold axes: 3 2.
Orthorhombic
a ≠ b ≠ c
sc, fcc, bcc, efcc = 4
2-fold axes: 3 3.
Tetragonal
a = b ≠ c
sc, bcc= 2
4-fold axis: 1

39. Rhombohedral or Trigonal
S.No.
System
Cell Dimensions
Crystal Angles
Bravais Lattices
Min. Sym. Elements 4.
Monoclinic
a ≠ b ≠ c
α = γ = 90ْ
β ≠ 90ْ
sc, efcc = 2
2-fold axis: 1 5.
Triclinic
α≠β≠γ≠ 90ْ
sc = 1
1-fold axis: 1 6.
Hexagonal
a = b ≠ c
α = β = 90ْ
γ = 120ْ
6-fold axis: 1 7.
Rhombohedral or Trigonal
a = b = c
α=β=γ≠ 90ْ
3-fold axis: 1

40. Examples of different crystal systems
S.No.
System
Example 1.
Cubic
NaCl, KCl, CaF2, Cu, ZnS, CsCl, Cu2O 2.
Orthorhombic
BaSO4, KNO3, MgSiO3, K2SO4, CdSO4, AgBr 3.
Tetragonal
SnO2, TiO2, ZrSiO4 4.
Monoclinic
CaSO4.2H2O, monoclinic S 5.
Triclinic
CuSO4.5H2O, NaHSO4, H3PO3 6.
Hexagonal
PbI2, Mg, Cd, Zn, ZnO, BN, SiO2, HgS, CdS 7.
Rhombohedral or Trigonal
Graphite, ICl, Al2O3, calcite (CaCO3), As, Sb, Bi

41. Cubic lattice

42. Orthorhombic lattice

43. Tetragonal lattices

44. Monoclinic lattice

45. Triclinic lattice

46. Hexagonal lattice

47. Rhombohedral (Trigonal) lattice

48. Structures of important ionic compounds
AB type: NaCl (rock salt)
CsCl
ZnS (zinc blende / sphalerite)
AB2 type: CaF2 (fluorite) TiO2 (rutile) SiO2
A2B type: K2O (antifluorite)

49. Structure of NaCl (Rock salt)
FCC type.
Co-ordination number 6:6.
Calculation of no. of atoms of NaCl/unit cell:
Cl at corners: (8  1/8) = 1
Cl at face centres (6  1/2) = 3
Na at edge centres (12  1/4) = 3
Na at body centre = 1
Unit cell contents are 4(Na+Cl-)
i.e. per each unit cell, 4 NaCl
units will be present.

50. Structure of sodium choride
Cubic unit cell:
smallest repeatable unit

51. Structure of CsCl bcc type. Co-ordination number 8:8.
Number of atoms/unit cell:1

52. Structure of ZnS fcc type. Co-ordination number 4:4.
Calculation of no. of
atoms/unit cell:
Total S = 8x1/8 + 6x1/2 = 4
Total Zn = 4
Hence, total ZnS = 4

53. Structure of CaF2 fcc type. Co-ordination number: 8:4
(8 for cation, 4 for anion)
*Note: All the compounds of AB2 type follow the same pattern.
Ca+ F-

54. Structure of K2O fcc type. Co-ordination number: 4:8 4 for cation
8 for anion
O -2
Na+

55. Structure of important covalent compounds
Diamond
Graphite

56. Diamond

57. Structure of diamond fcc type. Tetrahedral C-C bond length = 1.34A
Refractive index = 2.4
High dispersive power of light
Non-conductor of electricity
3d network
Hardest substance ever known.
Used as abrasive.

58. 3d- structure of diamond

59. Graphite

60. Structure of Graphite One of the softest substances ever known.
2-d hexagonal layer structure
C-C bond length = 1.45A
Inter layer distance = 3.54A
Sliding nature
sp2 hybridisation with one electron left over.
Specific gravity 2.2
Electrical conductor
Metallic lustre
Used as good lubricant.

61. 2d- structure of graphite

62. FULLURENES

63. Important points about Fullurenes
Discovered in 1985 as C60.
Consists of spherical, ellipsoid or cylindrical arrangement of dozens of C-atoms.
3 types:
Spherical: Also called ‘bucky balls’. Molecule of the year 1991 by Science magazine.
Cylindrical: C nanotubes or buckytubes.
Planar.

64. Structure of fullurenes
60 C-atoms arranged in pentagons and hexagons.
7Å in diameter.
Soccer-ball shaped molecule with 20 six-membered & 12 five-membered rings.
Each pentagon is surrounded by five hexagons.
No two pentagons are adjecent.
Each carbon is sp2-hybridized.
Used:
as photoresistant.
in the preparation of super-conductors.
in optical devices.
in batteries as charge carriers.

65. BRAGG’S EQUATION X-ray Tube Detector
Beam 2 lags beam 1 by XYZ = 2d sin 
so 2d sin  = n Bragg’s Law